Cross-efficiency in DEA: A maximum resonated appreciative model

• This paper provides an illustration of multiple optimal solutions for both efficient and inefficient DMUs.
• It deals with multiple optimal solution within the context of cross-efficiency models.
• It introduces a model that is most appreciative for all DMUs being cross-evaluated by all others.
• It proves the appreciative superiority of the method theoretically and numerically for a case of ranking in DEA.

The occurrence of multiple optimal solutions is an important and interesting issue in data envelopment analysis (DEA), for it allows flexibility to estimate the optimal cross-efficiencies of all decision making units (DMUs). This paper uses the advantage of multiple optimal solutions, be in the cases of efficient and/or inefficient DMUs, to integrate both the first and second-order voices of all DMUs and proposes a most appreciative cross-efficiency DEA method. The paper deals with multiple optimal solution cases within the context of cross-efficiency models and suggest a model that is most appreciative for all DMUs being cross-evaluated by all others. The merits and appreciative superiority of the proposed method is proven theoretically; and illustrated practically through a ranking study chosen from the literature.

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